Write the equation of the line that is parallel to 2x=1-3y and passes through (9,4).

The relationship between parallel lines is that they have the same slope. The equation of the line that is parallel to and passes through (9,4) is

Given that:

First, we make y the subject

Divide both sides by 3

A linear equation is represented as:

Where:

So, by comparison:

Parallel lines have the same slope.

So the slope of the line that passes through (9,4) is

The equation is then calculated as:

Where:

So, the equation becomes:

Expand

Hence, the equation of the line that is parallel to and passes through (9,4) is

Read more about equation of parallel lines at:

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< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)